4 citations · 15 across the 8 of their papers we have counts for
7 papers · 1 filter
Spectral Radius of Biased Random Walks on Regular Trees
He Song
We consider biased random walk on regular tree and we obtain the spectral radius, first return probability and -step transition probability.
Uniform spanning forests associated with biased random walks on Euclidean lattices
Zhan Shi, Vladas Sidoravicius, He Song +2
The uniform spanning forest measure () on a locally finite, infinite connected graph with conductance is defined as a weak limit of uniform spanning tree meas…
On Spectral Radius of Biased Random Walks on Infinite Graphs
Zhan Shi, Vladas Sidoravicius, He Song +2
We consider a class of biased random walks on infinite graphs and present several general results on the spectral radius of biased random walk.
Cutpoints for Random Walks on Quasi-Transitive Graphs
He Song, Kainan Xiang
We prove that a simple random walk on quasi-transitive graphs with the volume growth being faster than any polynomial of degree 4 has a.s. infinitely many cut times, and hence infi…
Monotonicity of the speed for biased random walk on Galton-Watson tree
Song He, Wang Longmin, Xiang Kainan
Ben Arous, Fribergh and Sidoravicius \cite{GAV2014} proved that speed of biased random walk on a Galton-Watson tree without leaves is strictly decreasing for $λ\leq \frac{m_…
Locality of percolation critical probabilities: uniformly nonamenable case
He Song, Kai-Nan Xiang, Song-Chao-Hao Zhu
Let be a sequence of transitive infinite connected graphs with where each is bond percolation critical pro…
Connective Constants on Cayley Graphs
He Song, Kai-Nan Xiang, Song-Chao-Hao Zhu
For a transitive infinite connected graph , let be its connective constant. Denote by the set of Cayley graphs for finitely generated infinite groups wi…